Method and system for automatic picking of borehole acoustic events based on new objective function

ABSTRACT

A method including obtaining, by a computer processor, a sonic waveform for each of a plurality of source and receiver positions along a borehole, and a sonic wave propagation velocity of a target event for the plurality of positions. Further, performing, a linear moveout correction on the sonic waveforms based on the velocity and stacking the linear moveout corrected waveforms to generate a stacked waveform at the plurality of positions. The method further includes determining an arrival-time of the target event on the stacked waveforms based on an extremum of a first objective and predicting a candidate arrival-time of the target event for the sonic waveform at the plurality positions based on the arrival-time of the target event on the stacked waveforms, and the sonic velocity. The method still further includes determining an arrival-time for the target event on the sonic waveform at the plurality positions within the borehole based on the candidate arrival-time of the target event and an extremum of a second objective function.

BACKGROUND

Engineers and geoscientists working in the oil and gas industryfrequently need to know the characteristics of sonic wave propagation insubsurface rock formations to inform their decision about whether, andwhere, to drill boreholes to find and produce hydrocarbons. To determinethese characteristics sonic tools may be deployed in borehole traversingthe subsurface rock formation suspended from the surface on wirelinecables or attached to drillstrings. Sonic tools typically have at leastone sonic source to generate sonic waves and a plurality of sonicreceivers to detect and record sonic waves.

To provide useful information about the subsurface rock formations sonicwave recordings may be processed to mitigate noise and determinecharacteristics of the sonic wave propagation including, withoutlimitation, sonic wave type, sonic wave propagation velocity, andarrival-time at the receiver.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

In general, in one aspect, embodiments relate to a method, includingobtaining, by a computer processor, a sonic waveform for each of aplurality of source and receiver positions along a borehole, and a sonicwave propagation velocity of a target event for the plurality ofpositions. Further, the method includes performing a linear moveoutcorrection on the sonic waveforms based on the sonic velocity, andstacking the linear moveout corrected waveforms to generate a stackedwaveform at the plurality of positions. The method further includesdetermining an arrival-time of the target event on the stacked waveformsbased on an extremum of a first objective and predicting a candidatearrival-time of the target event for the sonic waveform at the pluralitypositions based on the arrival-time of the target event on the stackedwaveforms, and the sonic velocity. The method still further includesdetermining an arrival-time for the target event on the sonic waveformat the plurality positions within the borehole based on the candidatearrival-time of the target event and an extremum of a second objectivefunction.

In general, in one aspect, embodiments relate to a non-transitorycomputer readable medium storing instructions executable by a computerprocessor, the instructions including functionality for obtaining asonic waveform for each of a plurality of source and receiver positionsalong a borehole, and a sonic wave propagation velocity of a targetevent for the plurality of positions. Further, the instructions includefunctionality for performing a linear moveout correction on the sonicwaveforms based on the sonic velocity, and stacking the linear moveoutcorrected waveforms to generate a stacked waveform at the plurality ofpositions. The instructions further include functionality fordetermining an arrival-time of the target event on the stacked waveformsbased on an extremum of a first objective and predicting a candidatearrival-time of the target event for the sonic waveform at the pluralitypositions based on the arrival-time of the target event on the stackedwaveforms, and the sonic velocity. The instructions still furtherinclude functionality for determining an arrival-time for the targetevent on the sonic waveform at the plurality positions within theborehole based on the candidate arrival-time of the target event and anextremum of a second objective function.

Other aspects and advantages of the claimed subject matter will beapparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be describedin detail with reference to the accompanying figures. Like elements inthe various figures are denoted by like reference numerals forconsistency.

FIG. 1 shows a sonic logging tool moving along a borehole in accordancewith one or more embodiments.

FIGS. 2A, 2B, 2C, and 2D show sonic waveforms, a spectrum, and sonicvelocity curve in accordance with one or more embodiments.

FIGS. 3A, 3B, 3C, and 3D show sonic waveforms in accordance with one ormore embodiments.

FIGS. 4A and 4B show stacked waveforms and objective function inaccordance with one or more embodiments.

FIGS. 5A and 5B show sonic waveforms and objective function inaccordance with one or more embodiments.

FIGS. 6A, 6B, 6C, and 6D show time-picks and QC metrics in accordancewith one or more embodiments.

FIG. 7 shows a flowchart, in accordance with one or more embodiments.

FIG. 8 shows a flowchart, in accordance with one or more embodiments.

FIGS. 9A and 9B show systems in accordance with one or more embodiments.

FIG. 10 shows a computer system, in accordance with one or moreembodiments.

DETAILED DESCRIPTION

In the following detailed description of embodiments of the disclosure,numerous specific details are set forth in order to provide a morethorough understanding of the disclosure. However, it will be apparentto one of ordinary skill in the art that the disclosure may be practicedwithout these specific details. In other instances, well-known featureshave not been described in detail to avoid unnecessarily complicatingthe description.

Throughout the application, ordinal numbers (e.g., first, second, third,etc.)

may be used as an adjective for an element (i.e., any noun in theapplication). The use of ordinal numbers is not to imply or create anyparticular ordering of the elements nor to limit any element to beingonly a single element unless expressly disclosed, such as using theterms “before”, “after”, “single”, and other such terminology. Rather,the use of ordinal numbers is to distinguish between the elements. Byway of an example, a first element is distinct from a second element,and the first element may encompass more than one element and succeed(or precede) the second element in an ordering of elements.

Embodiments disclosed herein relate to a novel method and system forobtaining an objective function that is efficient and robust forautomatic picking and tracking of borehole acoustic waveform events.This new objective function integrates four differentmeasures—semblance, phase, energy ratios and pick consistency—and servesas the kernel for a two-pass application of automatic picking schemesimplemented on a stacked waveform and a common-receiver-gather,respectively. More specifically, the new objective function is formed bya workflow including the following steps: first, linear moveoutcorrection is performed on each shot-gather to approximately align thesonic waveforms in time and the approximately aligned sonic waveformsare then stacked to highlight a target event. Next, a seed-point isdetermined, and using this data point, a first pass automatic eventpicking on the stacked waveform is performed to generate a 1D initialpick vector. Subsequently, an initial 2D event surface is obtained byextending the 1D initial pick vector to each receiver based on thevelocity information of the target wave. Lastly, the second pass ofautomatic picking is implemented on a common receiver configuration toyield the final result by optimizing the initial 2D event surface. Thesesteps will be explained below with respect to FIGS. 1-8.

FIG. 1 shows a sonic logging tool (102), in accordance with one or moreembodiments, at three different sonic source activation positions (108)within a borehole traversing a subsurface rock formation. A soniclogging tool (102) may be inserted into the borehole on a wirelinecable, on slick-line, as part of the bottomhole assembly (BHA) of adrillstring, on a wireline cable through drillpipe, or on coil tubing.In the exemplary embodiments shown, the sonic logging tool (102) has onesonic source (104) for controllably radiating sonic waves. In otherembodiments, the sonic logging tool (102) may have a plurality of sonicsources for controllably radiating sonic waves. In the exemplaryembodiments shown, the sonic tool has thirteen (13) sonic receivers(106) for detecting and recording propagating sonic waves. In otherembodiments, the sonic logging tool (102) may have a greater, or alesser number of sonic receivers. The sonic sources (104) may bepositioned at a single axial position on the sonic logging tool (102),in accordance with one or more embodiments. In other embodiments, thesonic sources (104) may be positioned at different axial positions onthe sonic logging tool (102). Typically, the sonic receivers (106) maybe spaced uniformly (112), with a spacing between 2 inches and 8 inches.However, in other cases, the sonic receiver (106) spacing may beirregular and/or random.

The sonic logging tool (102 may be operated by activating the sonicsource (104) at a particular axial position within the borehole, and ata particular activation time. After activating the sonic source (104), asonic wave is emitted by the sonic source, and this sonic wave may besubsequently detected and recorded at each of the sonic receivers (106)over a subsequent time-window. More specifically, a time-series of sonicwave amplitudes is detected and recorded by the sonic receivers (106).The sonic logging tool (102) may then be moved axially along theborehole and the sonic source (104) activation and sonic receiver (106)detection and recording procedure repeated at adjacent positions alongthe borehole (108). The sonic source (104) firing and the sonic receiver(106) detection and recording may occur while the sonic logging tool(102) is stationary within the borehole, but more typically, the sonicsource (104) firing and the sonic receiver (106) detection and recordingmay occur while the sonic logging tool (102) is in continuous axialmotion along the borehole. Generally, the axial separation between thesonic source activation positions (108) are separated by a uniformincrement (110) which may be similar to the distance between sonicreceiver (106) positions in the sonic logging tool (102).

The time-series of sonic disturbance amplitudes recorded by each sonicreceiver (106) for each sonic source (104) activation is denoted as a“sonic waveform”. In accordance with one or more embodiments thedisturbance amplitude recorded by each sonic receiver (106) may be apressure, or a pressure fluctuation caused by the sonic wave. In otherembodiments, the disturbance amplitude may be particle velocity, orparticle acceleration.

FIG. 2A shows an array of sonic waveforms (220), in accordance with oneor more embodiments. The sonic disturbance amplitude is shown on thegrayscale (222A), the abscissa enumerates the sonic receiver index(114), and the ordinate shows the elapsed time after the activation ofthe sonic source. Each column of FIG. 2A depicts the waveform recordedby one sonic receiver of the receiver index (214) that makes up thex-axis of the graph shown. The sonic receiver (106) with index=1 islocated closest to the sonic source (104), and the sonic receiver (106)with index=13 is located furthest from the sonic source (104). In FIG.2A, the 13 sonic waveforms (220) shown are recorded by 13 sonicreceivers (106) located adjacent to one another on the sonic loggingtool (102). The sonic waveforms (220) shown in FIG. 2A are caused by asingle activation of a sonic source. The first arriving sonic wave (226)can be seen passing the plurality of sonic receivers, starting atapproximately 0/9 milliseconds (msec) at the sonic receiver (106) withindex=1 and ending at approximately 1.3 msec at the sonic receiver (106)with index=13. Later arriving sonic waves contribute to the sonicwaveforms at later times.

FIG. 2B shows an exemplary embodiment of the normalized spectralamplitude (230) of one of the sonic waveforms (220) shown in FIG. 2A. Inthe example of FIG. 2B, the maximum normalized spectral amplitude (230)is located at approximately 7 kHz. In other embodiments, the maximumnormalized spectral amplitude (230) may be at a lower frequency, such as2 kHz or lower, or at a higher frequency, such as 20 kHz or higher.

FIG. 2C shows the sonic waveform recorded by the sonic receiver withindex=1 (228), for a plurality of sonic source activation positions(108) along the borehole (108). In FIG. 2C the sonic disturbanceamplitude is shown on the grayscale (222B), the abscissa shows theelapsed time after the activation of the sonic source (104), and theordinate enumerates the sonic source activation positions along theborehole (108). Each row of FIG. 2C depicts the waveform recorded by thesonic receiver (106) with index=1, for a single firing of the sonicsource (104). Each waveform shown in FIG. 2C corresponds to a sonicsource—sonic receiver geometry with the same spatial separation betweenthe sonic source (104) and sonic receiver (106). Since the sonic source(104) and sonic receiver (106) are both rigidly attached to the soniclogging tool (102), the sonic receiver (106) moves from one axialposition in the borehole to the next axial position at the same rate atwhich the sonic source (104) moves from one axial position to the nextaxial position. Thus, the spatial distance between the sonic source(104) and the sonic receiver (106) remain unchanged.

On each sonic waveform (228) at early time the sonic disturbanceamplitude varies smoothly and slowly with time. This is themanifestation of low temporal-frequency noise on the sonic waveform. Alittle before an elapsed time of 1 msec the character of the sonicwaveform (228) changes, showing a rapid oscillation of amplitude. Thisrapid oscillation is the manifestation of the first arriving sonic wave(232) on the sonic waveform (228). Later in the sonic waveform (228)more subtle changes in oscillation amplitude and frequency occur. Theselater changes are the manifestation of later arriving sonic waves on thesonic waveform (220).

The first arriving sonic wave (232 ) visible on FIG. 2C arrives atdifferent times for different sonic source activation positions (108),even though the sonic source ((104)) to sonic receiver (106) spatialseparation remains unchanged, as described above. Thus, one may concludethat the changing arrival-time of the first arriving sonic wave (232) isdue to a change sonic wave propagation velocity (234) of the subsurfacerock formation at different sonic source activation positions (108)along the borehole. An exemplary embodiment of the sonic wavepropagation velocity (234) is shown in FIG. 2D.

FIG. 3A shows the same sonic waveforms (320) depicted in FIG. 2A. Inaddition to the sonic waves visible (338) in the later portion of thesonic waveforms (320), low frequency sonic noise (340) is visible in theearlier portion of the sonic waveforms (320). In many cases, the lowfrequency noise (340) is also present in the later portions of the sonicwaveforms (320), but masked or less visible because of the presence ofthe sonic waves (338). In accordance with one or more embodiments, thesonic waveforms (320) may be band-pass filtered to remove the lowfrequency noise (340), to produce band-passed sonic waveforms (342)shown in FIG. 3B.

In accordance with one or more embodiments, a linear moveout correctionmay be applied to a plurality of sonic waveforms (320, 342) resultingfrom a single activation of the sonic source (104). A linear moveoutcorrection includes selecting a sonic wave propagation velocity (234 )for a target event. The target event may be a first arriving sonic wave(232 ), or the target event may a later arriving, and slowerpropagating, sonic wave. The sonic wave propagation velocity (234),V_(T), is specified as input to the linear moveout correction. Inaccordance with one or more embodiments, v_(T) may be determined fromprior analysis of the sonic waveforms (320, 343), or in accordance withother embodiments, v_(T) may be selected from a group of trial values ofthe sonic wave propagation velocity (234 ). A linear moveout correctionmay align, or approximately, align in time the target event on each ofthe sonic waveforms.

In addition, in accordance with one or more embodiments, a referencesonic source (104) to sonic receiver (106) distance, x₀, may bespecified as input to the linear moveout correction. Frequently, x₀ maybe chosen to be the distance between the sonic source (104) and thesonic receiver (106), but many other values of x₀ may be used. Thelinear moveout correction may then be applied by shifting the elapsedtime of each sample of the sonic waveform to an earlier time, whereinthe duration of the shift, Δt_(i), for the sonic waveform with index=i,is given by:

Δt _(i)=(x _(i) −x ₀)v _(T)  Equation (1)

where x_(i) is the distance between the sonic source (104) and thei^(th) sonic receiver. FIG. 3C shows the linear moveout corrected sonicwaveforms (344) obtained by applying a linear moveout correction to theband-pass filtered sonic waveforms shown in FIG. 3B. FIG. 3C shows theapproximately align in time of the target event on each of the sonicwaveforms after linear moveout correction.

In accordance with one or more embodiments, the linear moveout correctedsonic waveforms (344) may be combined in a process denoted “stacking” toproduce a stacked waveform (346). Many forms of stacking are known toone of ordinary skill in the art. A simple implementation of stacking,according to one or more embodiments involves summing the n^(th) samplefrom each waveform to be stacked to give the value of the n^(th) samplein the stacked waveform (346). For example, the 1^(st) sample from eachwaveform to be stacked are summed to obtain the 1^(st) sample in thestacked waveform (346). Similarly, the 11^(th) sample from each waveformto be stacked are summed to obtain the 11^(th) sample in the stackedwaveform (346).

In other embodiments, the operation of summing the sample may bereplaced by averaging the samples. For example, the averaging operationmay include, without limitation, forming the mean, mode, median,harmonic mean, geometric mean, weighted-mean, weighted-mode,weighted-median, weighted-harmonic mean, weighted-geometric mean,trimmed-mean, trimmed-median, trimmed-harmonic mean, ortrimmed-geometric mean.

FIG. 3D shows the stacked waveform (346) resulting from stacking thelinear moveout corrected, band-pass filtered sonic waveforms shown inFIG. 3C. In FIG. 3D the same stacked waveform (346) has been displayedin 13-fold duplicate side-by-side to facilitate comparison with thesonic waveforms (320) in FIG. 3A, the band-pass filtered sonic waveforms(342) in FIG. 3B, and the linear moveout corrected waveforms (344) inFIG. 3C.

In accordance with one or more embodiments, FIG. 4A shows the stackedwaveforms (446) for a plurality of sonic source activation positionsalong the borehole (108). In addition, in accordance with one or moreembodiments, FIG. 4A shows a seed-point (448) specified on one selectedstacked waveform (446) chosen from the plurality of stacked waveforms(446). Picking the arrival-time (452) of the target event on the stackedwaveforms (446) may proceed iteratively from the stacked waveform onwhich the seed-point (448) is selected, to a lower index (shallower)stacked waveform, and to a greater index (deeper) stacked waveform. Thestacked waveform on which the arrival-time of the target event is to bepicked may be denoted the current waveform, C (it), where it indexestime samples. After the arrival-time (452) of the target event has beenpicked on the current waveform, the current waveform may be time-shiftedto align the target event with the previously picked target event onother stacked waveforms (446). The time-shifted current waveform may beadded to a group of arrival-time aligned stacked waveforms (446),denoted reference waveforms, R(it, iz), where iz indexes axial positionalong the borehole (depth) samples. The arrival-time (452) of the targetevent on each of the reference waveforms are aligned with one another.

In some embodiments, a current waveform may be selected as the stackedwaveform closest in axial borehole position to the reference waveformsabove (at a shallower depth) the reference waveforms. In otherembodiments, the current waveform may be the closest stacked waveform tothe reference waveforms below (at a deeper depth) the referencewaveforms.

In accordance with one or more embodiments, a first time-window (450)may be selected surrounding the seed-point (448), as shown in FIG. 4A.The first time-window (450) may be symmetrically disposed around theseed-point (448), such that the seed-point (448) is located at thecenter of the first time-window (450) , or in other embodiments thefirst time-window (450) may be asymmetrically disposed around theseed-point (448). In accordance with one or more embodiments, theduration first time-window (450) may be chosen to enclose between 4 and6 cycles of the stacked waveforms (446).

In accordance with one or more embodiments, a first objective function(454) may be formed from the samples of the current waveform and thereference waveforms. The first objective function (454), O₁, may bewritten as:

O₁=(W _(S1)M_(S) +w _(P1) M _(P) +w _(R1) M _(R))*M _(C)  Equation (2)

where w_(s1), w_(p1), and w_(R1) are scalar weights, which may beselected by the user. These weights may be selected to differ from oneanother, or they may be selected to be identical to one another. All theweights may be select to be unity.

The vector M_(S)(dt) quantifies the semblance between the currentstacked waveform, C(it), and the reference waveform, R(it, iz), and maybe written as:

$\begin{matrix}{{M_{S}({dt})} = {\sum\limits_{it}{\sum\limits_{iz}\frac{\left( {{R\left( {{it},{iz}} \right)} + {C\left( {{it} - {dt}} \right)}} \right)^{2}}{\left( {{R\left( {{it},{iz}} \right)}^{2} + {C\left( {{it} - {dt}} \right)}^{2}} \right)}}}} & {{Equation}\mspace{14mu}(3)}\end{matrix}$

where dt is a time-shift between the current waveform and the referencewaveforms, and the summation over it includes the time samples withinthe first time-window (450), and the summation over iz includes aportion of the reference waveforms. The portion of the referencewaveforms may include one or more of the reference waveforms closest tothe current waveform.

The vector M_(p)(dt) quantifies the phase consistency between thecurrent stacked waveform and the reference waveform and may be writtenas:

$\begin{matrix}{{M_{P}({dt})} = {\sum\limits_{it}\frac{1}{{\sum\limits_{iz}{{{R\left( {{it},{iz}} \right)} - {C\left( {{it} - {dt}} \right)}}}} + \mu}}} & {{Equation}\mspace{14mu}(4)}\end{matrix}$

where μ is a small pre-whitening scalar, introduced to ensure numericalstability, and the summation over it includes the time samples withinthe first time-window (450), and the summation over iz includes aportion of the reference waveforms. The portion of the referencewaveforms may include one or more of the reference waveforms closest tothe current waveform.

The vector M_(R)(dt) quantifies the differences in the energy ratiobetween the current waveform and the reference waveform and may bewritten as:

$\begin{matrix}{{M_{R}({dt})} = {1 - \frac{\sum\limits_{iz}{{{E_{R}\left( {iz} \right)} - E_{C}}}}{\sum\limits_{iz}\left( {{E_{R}\left( {iz} \right)} + E_{C}} \right)}}} & {{Equation}\mspace{14mu}(5)}\end{matrix}$

where E_(R)(iz) and E_(C) are the energy ratios of the referencewaveforms and the current waveform within the first time-window (450),respectively, and the summation over iz includes a portion of thereference waveforms. The portion of the reference waveforms may includeone or more of the reference waveforms closest to the current waveform.

The vector M_(C)(dt) quantifies the pick consistency between the currentstacked waveform and the reference waveform and may be written as:

$\begin{matrix}{{M_{C}({dt})} = \frac{1}{1 + M_{j}}} & {{Equation}\mspace{14mu}(6)}\end{matrix}$

wherein:

$\begin{matrix}{{{M_{j}({dt})} = {\frac{1}{T_{C}*{Nz}}{\sum\limits_{iz}\left. {{P_{R}({iz})} - {dt}} \right)}}}} & {{Equation}\mspace{14mu}(7)}\end{matrix}$

where P_(R)(iz) is the arrival-time (452) picked for the iz ^(th)reference waveform, dt, is the candidate time-shift of the currentwaveform. t_(c) is the duration of one period of the peak frequency ofthe waveform spectrum and N_(Z) is the number of waveforms in theportion of reference waveforms included in the summation.

In accordance with one or more embodiments, the value of the firstobjective function (454), O₁, is determined for a range of values of thetime-shift dt. The time-shift may include both positive and negativetime-shifts, or may include either positive or negative time-shifts. Inaccordance with one or more embodiments, the maximum value of O₁, may bedetermined and the value of the time-shift, dt, at which this maximum islocated is the added to the arrival time of the target event in thereference waveforms to determine the arrival time of the target event inthe current waveform. The time-shifted current waveform may be added tothe previously identified reference waveforms, and a new currentwaveform selected.

One of ordinary skill in the art will readily appreciate that the firstobjective function (454) shown in equation (2) may be modified tobecome:

=L−(w _(S) M _(S) +w _(p) M _(p) +w _(R) M _(R))*M _(C)  Equation (9)

where L is any sufficiently large scalar value. The process of finding amaximum of O₁ given by equation (2) is now completely equivalent to theprocess of finding a minimum of

given by equation (9). Those skilled in the art will appreciate thatregardless of the variations and/or alternate forms of the objectivefunction that may be employed, the overall scope of the invention is notsubstantively changed.

In accordance with one or more embodiments, FIG. 4B shows the value ofthe first objective function (454 obtained using equation (2), togetherwith the seed-point (448) and the first time-window (450) surroundingthe seed-point (448). The value of the objective function is shown onthe grayscale. The white line represents the maximum of the firstobjective function (456) for each of the stacked waveforms (446). Thepicked arrival-time (452) for the target event for each of the stackedwaveforms (446) is plotted on FIG. 4A.

According to one or more embodiments, after the arrival-time (452) forthe target event, T_(st)(iz), has been determined for a plurality ofstacked waveforms (446), a “candidate” arrival-time for the target eventon a sonic waveform, T_(cand)(j, iz), at each of a plurality of sonicreceivers (106) may be determined as:

T _(cand)(j,iz)=T _(st)(iz)+(x _(j)-x ₀)v _(T)  Equation (10)

where x_(j) is the sonic source (104) to sonic receiver (106) distancefor the j^(th) sonic receiver, x₀ is the sonic source (104) to stackedwaveform position, and v_(T) is the target event velocity, as describedin equation (1). T_(cand)(j, iz) is denoted the expected candidatearrival-time of the target event on waveform of the j^(th) sonicreceiver (106) for the iz^(th) sonic source activation, based upon thearrival-time (452) of the target event on the stacked waveforms (446)and the selected target event sonic wave propagation velocity (234).

FIG. 5A shows the sonic waveforms for the 3^(rd) sonic receiver (546)(see FIG. 1), in accordance with one or more embodiments. FIG. 5A alsoshows the candidate arrival-time (548) for the target event, T_(cand) onone sonic waveform for the 3^(rd) sonic receiver (546). FIG. 5A alsoshows a second time-window (550). The second time-window (550) may beselected surrounding the candidate arrival-time (548), T_(cand),as shownin FIG. 5A. The second time-window (550) may be symmetrically disposedaround the candidate arrival-time (548), T_(cand), such that thecandidate arrival-time (548), T_(cand), is located at the center of thesecond time-window (550), or in other embodiments the second time-window(550) may be asymmetrically disposed around the candidate arrival-time(548), T_(cand). In accordance with one or more embodiments, theduration second time-window (550) may be chosen to be of lesser durationthan the first time-window (450), although in other embodiments thesecond time-window (550) may be of the same or longer duration than thefirst time-window (450).

Picking the arrival-time (552) of the target event, T_(pick), on aplurality of sonic waveforms for the 3^(rd) sonic receiver (546) mayproceed iteratively. In accordance with one or more embodiments, thesonic waveform for the 3^(rd) sonic receiver (546) on which a candidatearrival-time (548) of a target event is selected may initiate theiterative procedure. Next, a lower index (shallower) sonic waveform forthe 3^(rd) sonic receiver (546), or a greater index (deeper) sonicwaveform for 3^(rd) sonic receiver (546), may be chosen. The sonicwaveform for the 3^(rd) sonic receiver (546) on which the arrival-time(552) of the target event, T_(pick), is to be picked may be denoted thecurrent waveform, C(it), where it indexes time samples. After thearrival-time (552) of the target event, T_(pick), has been picked on thecurrent waveform, the current waveform may be time-shifted to align thetarget event with the previously picked arrival-time of the target eventon other sonic waveforms for the 3^(rd) sonic receiver (546). Thetime-shifted current waveform may be added to a group of arrival-timealigned sonic waveforms, denoted reference waveforms, R(it, iz), whereiz indexes sonic source positions along the borehole (108). Thearrival-time (552) of the target event on each of the referencewaveforms are aligned with one another.

In some embodiments, a current waveform may be selected as the sonicwaveform for the 3^(rd) sonic receiver (546) closest in axial boreholeposition to the reference waveforms above (at a shallower depth) thereference waveforms. In other embodiments, the current waveform may bethe closest sonic waveform for the 3^(rd) sonic receiver (546) to thereference waveforms below (at a deeper depth) the reference waveforms.

In accordance with one or more embodiments, a second objective function(554) may be formed from the samples of the current waveform and thereference waveforms. The second objective function (454), O₂, may bewritten as:

O ₂=(w _(S2) M _(S) +w _(P2) M _(P) +w _(R2) M _(R))*M _(C)  Equation(10)

where w_(s2), w_(p2), and w_(R2) are scalar weights, which may beselected by the user. These weights may be selected to differ from oneanother, or they may be selected to be identical to one another. All theweights may be select to be unity. In accordance with one or moreembodiments, the weights w_(s2), w_(p2), and w_(R2) may be selected tobe the same as the weights w_(s1), w_(p1), and w_(R1) respectively, orin other embodiments they be selected to be different. The functionsM_(S), M_(P), M_(R) and M_(C) retain the same meaning as defined earlierin equations (3), (4), (5), (6) and (7).

Just as the first objective function (454), O₁, from equation (2) couldbe modified to become

in equation (9) above, so the second objective function (554), O₂, canbe similarly modified. Those skilled in the art will appreciate thatregardless of the variations and/or alternate forms of the objectivefunction that may be employed, the overall scope of the invention is notsubstantively changed.

In accordance with one or more embodiments, the value of the secondobjective function (554), O₂, is determined for a range of values of thetime-shift dt. The time-shift may include both positive and negativetime-shifts, or may include either positive or negative time-shifts. Inaccordance with one or more embodiments, the maximum value of O₂, may bedetermined and the value of the time-shift, dt, at which this maximum islocated is the added to the arrival time of the target event in thereference waveforms to determine the arrival time (552) of the targetevent, T_(pick), in the current waveform. The time-shifted currentwaveform may be added to the previously identified reference waveforms,and a new current waveform selected.

In accordance with one or more embodiments, after the completion of thepicking of the arrival-time (552) of the target event, T_(pick), on aplurality of sonic waveforms for the 3^(rd) sonic receiver (546), thearrival-time of the target event, T_(pick), may be picked on a pluralityof sonic waveforms for other sonic receivers, such as the 1^(st) ,2^(nd), or 10^(th) sonic receivers. In accordance with one or moreembodiments, the arrival-time (552) may be picked on each sonic receiverin turn, beginning with the 1^(st) sonic receiver. In other embodiments,the arrival-time (552) may be picked on each sonic receiver in anyorder. In other embodiments, the arrival-time (552) of the target event,T_(pick), may be picked on a plurality of sonic waveforms for all sonicreceivers simultaneously.

In accordance with one or more embodiments, FIG. 6A shows the finalpicked arrival-times (652) for the target event for all sonic receivers(106) and all sonic source activation positions along the borehole(108), T_(pick)(j, iz), where 1≤j≤Nr, and Nr denotes the total number ofaxial receiver positions on the sonic logging tool (102), and 1≤iz≤Ns,and Ns equals the number of sonic source activation positions along theborehole (108). In the example shown in FIG. 6A, Ns=1200. FIG. 6B showsthe same final picked arrival-times (652) of the target event in adifferent format. Each line shows the final picked arrival-times (652)of the target event for a single sonic receiver (106) at a plurality ofdifferent sonic source activation positions along the borehole (108).

In accordance with one or more embodiments, quality control metrics maybe determined for the final picked arrival-times of the target event.FIG. 6C shows one such quality control metric. FIG. 6C shows the maximumvalue of the second objective function (654) for each sonic receiver(106) and sonic source activation positions along the borehole (108).FIG. 6C offers an important quality control metric and indicate thereliability of the final picked arrival-times (652) of the target event.Light shades indicate a large relative value of the maximum value secondobjective function (654), and hence a reliable final pickedarrival-time. In contrast, dark shades indicate a small relative valueof the maximum value of the second objective function (654), and hence aless reliable final picked arrival-time.

FIG. 6D shows statistical quality control metrics in accordance with oneor more embodiments. The solid curve shows the mean of the maximum valueof the second objective function averaged over sonic receivers (106) foreach sonic source activation positions along the borehole (108). FIG. 6Dalso shows the mean value plus and minus twice the standard deviation(662) of the value of second objective function displayed FIG. 6C asdashed lines. The presence of fractures, borehole breakouts andlithology transitions may the main contributors to the uncertainties inthe final picks.

FIG. 7 shows a flowchart in accordance with one or more embodiments.Specifically, FIG. 7 describes in detail the steps of the workflow tocreate the objective function described above. Further, one or moreblocks in FIG. 7 may be performed by one or more components as describedin FIG. 10 (e.g., computing system 1000 including computer processor(s)1004 and communication interface 1008). While the various blocks in FIG.7 are presented and described sequentially, one of ordinary skill in theart will appreciate that some or all of the blocks may be executed indifferent orders, may be combined or omitted, and some or all of theblocks may be executed in parallel. Furthermore, the blocks may beperformed actively or passively.

In Block 702, sonic waveforms for a plurality of source and receiverpositions within a borehole are obtained from a survey acquired with asonic logging tool. In accordance with one or more embodiments, in Block704, a band-pass filter may be applied to the sonic waveforms acquiredin Block 702. In other embodiments, the sonic waveforms may not beband-passed filtered.

In Block 706, a borehole sonic velocity curve for a plurality of sourcepositions within a borehole is obtained. In one or more embodiments, thesonic velocity curve may be obtained from the sonic waveforms obtainedin Block 702, either before or after band-pass filtering. In accordancewith other embodiments, the sonic velocity curve may be obtained fromother measurements.

In Block 708, a linear moveout correction on the sonic waveforms isperformed based, at least in part, on the sonic velocity of a targetevent. Further, in Block 708 the moveout corrected waveforms may bestacked to generate a stacked waveform for each of the plurality ofpositions.

In Block 710, an arrival-time on the stacked waveform for each of theplurality of positions is determined based, at least in part, on anextremum of a first objective function (454). The determination of theextremum is depicted in more detail in, and described in the context of,FIG. 8.

In accordance with one or more embodiments, in Block 712, a candidatearrival-time for a target event on a sonic waveforms at a plurality ofsource and receiver positions is predicted based, at least in part, onthe stacked waveform arrival times, and the sonic velocity of a targetevent. In the preferred embodiment, the candidate arrival-time may bepredicted assuming a linear moveout of the target event across the arrayof sonic receivers.

In Block 714, in accordance with one or more embodiments, anarrival-time of a target event on a sonic waveform at a plurality ofsource and receiver positions is determined based on the candidatearrival-time pick of the target event and an extremum of a secondobjective function. The second objective function may have the samefunctional form as the first objective function (454), in accordancewith some embodiments. In accordance with other embodiments, the secondobjective function may have a different functional form from the firstobjective function (454). In either case, the first objective function(454) takes stacked waveforms (446) as input variables, whereas secondobjective function takes sonic waveforms as input variables.

FIG. 8 shows a flowchart, in accordance with one or more embodiments,which discloses the steps leading to determining an arrival-time of atarget event using the extremum of an objective function. FIG. 8 appliesequally to the first objective function (454) disclosed in equation (2)when the waveforms are stacked waveforms (446), and the second objectivefunction disclosed in equation (10) when the waveforms are sonicwaveforms.

In Block 802, in accordance with one or more embodiments, an initialwaveform is selected, together with an arrival-time of a target event onthe initial waveform, and a time-window surrounding the arrival-time.Further the initial waveform is defined to be a reference waveform.

In Block 804, in accordance with one or more embodiments, a currentwaveform is selected adjacent to the reference waveform, and anobjective function based on the reference waveform and the currentwaveform is evaluated for a plurality of time-shifts between them, andan extremum of the objective function is determined. The extremum may bea maximum, or a minimum, depending on the form selected for theobjective function as disclosed in equation (2) and equation (9).

In accordance with one or more embodiments, in Block 806, thearrival-time of the target event on the current waveform is identifiedas the sum of the arrival-time on the reference waveform, and thetime-shift of the extremum of the objective function.

In Block 808, in accordance with one or more embodiments, the workflowchecks to determine if the current waveform is the final waveform forwhich an arrival-time of a target event is required. If the currentwaveform is the final waveform then the workflow may be terminated inBlock 810. If the current waveform is not the final waveform for whichan arrival-time of a target event is required, then the workflow mayproceed to Block 812.

In Block 812, in accordance with one or more embodiments, the currentwaveform may be time-shifted to align the target event with the targetevent in the reference waveforms, and the time-shifted current waveformis added to the plurality of reference waveforms.

FIGS. 9A and 9B illustrate systems in accordance with one or moreembodiments. As shown in FIG. 9A, a drilling system (900) may include atop drive drill rig (910) arranged around the setup of a drill bitlogging tool (920). A top drive drill rig (910) may include a top drive(911) that may be suspended in a derrick (912) by a travelling block(913). In the center of the top drive (911), a drive shaft (914) may becoupled to a top pipe of a drill string (915), for example, by threads.The top drive (911) may rotate the drive shaft (914), so that the drillstring (915) and a drill bit logging tool (920) cut the rock at thebottom of a wellbore (916). A power cable (917) supplying electric powerto the top drive (911) may be protected inside one or more service loops(918) coupled to a control system (944). As such, drilling mud may bepumped into the wellbore (916) through a mud line, the drive shaft(914), and/or the drill string (915).

Moreover, when completing a well, casing may be inserted into thewellbore (916). The sides of the wellbore (916) may require support, andthus the casing may be used for supporting the sides of the wellbore(916). As such, a space between the casing and the untreated sides ofthe wellbore (916) may be cemented to hold the casing in place. Thecement may be forced through a lower end of the casing and into anannulus between the casing and a wall of the wellbore (916). Morespecifically, a cementing plug may be used for pushing the cement fromthe casing. For example, the cementing plug may be a rubber plug used toseparate cement slurry from other fluids, reducing contamination andmaintaining predictable slurry performance. A displacement fluid, suchas water, or an appropriately weighted drilling mud, may be pumped intothe casing above the cementing plug. This displacement fluid may bepressurized fluid that serves to urge the cementing plug downwardthrough the casing to extrude the cement from the casing outlet and backup into the annulus.

As further shown in FIG. 9A, sensors (921) may be included in a sensorassembly (923), which is positioned adjacent to a drill bit (924) andcoupled to the drill string (915). Sensors (921) may also be coupled toa processor assembly (923) that includes a processor, memory, and ananalog-to-digital converter (922) for processing sensor measurements.For example, the sensors (921) may include acoustic sensors, such asaccelerometers, measurement microphones, contact microphones, andhydrophones. Likewise, the sensors (921) may include other types ofsensors, such as transmitters and receivers to measure resistivity,gamma ray detectors, etc. The sensors (921) may include hardware and/orsoftware for generating different types of well logs (such as acousticlogs or density logs) that may provide well data about a wellbore,including porosity of wellbore sections, gas saturation, bed boundariesin a geologic formation, fractures in the wellbore or completion cement,and many other pieces of information about a formation. If such welldata is acquired during drilling operations (i.e.,logging-while-drilling), then the information may be used to makeadjustments to drilling operations in real-time. Such adjustments mayinclude rate of penetration (ROP), drilling direction, altering mudweight, and many others drilling parameters.

In some embodiments, acoustic sensors may be installed in a drillingfluid circulation system of a drilling system (900) to record acousticdrilling signals in real-time. Drilling acoustic signals may transmitthrough the drilling fluid to be recorded by the acoustic sensorslocated in the drilling fluid circulation system. The recorded drillingacoustic signals may be processed and analyzed to determine well data,such as lithological and petrophysical properties of the rock formation.This well data may be used in various applications, such as steering adrill bit using geosteering, casing shoe positioning, etc.

The control system (944) may be coupled to the sensor assembly (923) inorder to perform various program functions for up-down steering andleft-right steering of the drill bit (924) through the wellbore (916).More specifically, the control system (944) may include hardware and/orsoftware with functionality for geosteering a drill bit through aformation in a lateral well using sensor signals, such as drillingacoustic signals or resistivity measurements. For example, the formationmay be a reservoir region, such as a pay zone, bed rock, or cap rock.

Turning to geosteering, geosteering may be used to position the drillbit (924) or drill string (915) relative to a boundary between differentsubsurface layers (e.g., overlying, underlying, and lateral layers of apay zone) during drilling operations. In particular, measuring rockproperties during drilling may provide the drilling system (900) withthe ability to steer the drill bit (924) in the direction of desiredhydrocarbon concentrations. As such, a geosteering system may usevarious sensors located inside or adjacent to the drilling string (915)to determine different rock formations within a wellbore's path. In somegeosteering systems, drilling tools may use resistivity or acousticmeasurements to guide the drill bit (924) during horizontal or lateraldrilling.

Turning to FIG. 9B, FIG. 9B illustrates some embodiments for steering adrill bit through a lateral pay zone using a geosteering system (990).As shown in

FIG. 9B, the geosteering system (990) may include the drilling system(900) from FIG. 9A. In particular, the geosteering system (990) mayinclude functionality for monitoring various sensor signatures (e.g., anacoustic signature from acoustic sensors) that gradually or suddenlychange as a well path traverses a cap rock (930), a pay zone (940), anda bed rock (950). Because of the sudden change in lithology between thecap rock (930) and the pay zone (940), for example, a sensor signatureof the pay zone (940) may be different from the sensor signature of thecap rock (930). When the drill bit (924) drills out of the pay zone(940) into the cap rock (930), a detected amplitude spectrum of aparticular sensor type may change suddenly between the two distinctsensor signatures. In contrast, when drilling from the pay zone (940)downward into the bed rock (950), the detected amplitude spectrum maygradually change.

During the lateral drilling of the wellbore (916), preliminary upper andlower boundaries of a formation layer's thickness may be derived from ageophysical survey and/or an offset well obtained before drilling thewellbore (916). If a vertical section (935) of the well is drilled, theactual upper and lower boundaries of a formation layer (i.e., actual payzone boundaries (A, A′)) and the pay zone thickness (i.e., A to A′) atthe vertical section (935) may be determined. Based on this well data,an operator may steer the drill bit (924) through a lateral section(960) of the wellbore (916) in real time. In particular, a logging toolmay monitor a detected sensor signature proximate the drill bit (924),where the detected sensor signature may continuously be compared againstprior sensor signatures, e.g., of the cap rock (930), pay zone (940),and bed rock (950), respectively. As such, if the detected sensorsignature of drilled rock is the same or similar to the sensor signatureof the pay zone (940), the drill bit (924) may still be drilling in thepay zone (940). In this scenario, the drill bit (924) may be operated tocontinue drilling along its current path and at a predetermined distance(0.5h) from a boundary of a formation layer. If the detected sensorsignature is same as or similar to the prior sensor signatures of thecap rock (930) or the bed rock (950), respectively, then the controlsystem (944) may determine that the drill bit (924) is drilling out ofthe pay zone (940) and into the upper or lower boundary of the pay zone(940). At this point, the vertical position of the drill bit (924) atthis lateral position within the wellbore (916) may be determined andthe upper and lower boundaries of the pay zone (940) may be updated,(for example, positions B and C in FIG. 9B). In some embodiments, thevertical position at the opposite boundary may be estimated based on thepredetermined thickness of the pay zone (940), such as positions B′ andC′.

While FIGS. 9A, and 9B shows various configurations of components, otherconfigurations may be used without departing from the scope of thedisclosure. For example, various components in FIGS. 9A, and 9B may becombined to create a single component. As another example, thefunctionality performed by a single component may be performed by two ormore components.

Embodiments may be implemented on a computer system. FIG. 10 is a blockdiagram of a computer system (1002) used to provide computationalfunctionalities associated with described algorithms, methods,functions, processes, flows, and procedures as described in the instantdisclosure, according to an implementation. The illustrated computer(1002) is intended to encompass any computing device such as a server,desktop computer, laptop/notebook computer, wireless data port, smartphone, personal data assistant (PDA), tablet computing device, one ormore processors within these devices, or any other suitable processingdevice, including both physical or virtual instances (or both) of thecomputing device. Additionally, the computer (1002) may include acomputer that includes an input device, such as a keypad, keyboard,touch screen, or other device that can accept user information, and anoutput device that conveys information associated with the operation ofthe computer (1002), including digital data, visual, or audioinformation (or a combination of information), or a GUI.

The computer (1002) can serve in a role as a client, network component,a server, a database or other persistency, or any other component (or acombination of roles) of a computer system for performing the subjectmatter described in the instant disclosure. The illustrated computer(1002) is communicably coupled with a network (1030). In someimplementations, one or more components of the computer (1002) may beconfigured to operate within environments, includingcloud-computing-based, local, global, or other environment (or acombination of environments).

At a high level, the computer (1002) is an electronic computing deviceoperable to receive, transmit, process, store, or manage data andinformation associated with the described subject matter. According tosome implementations, the computer (1002) may also include or becommunicably coupled with an application server, e-mail server, webserver, caching server, streaming data server, business intelligence(BI) server, or other server (or a combination of servers).

The computer (1002) can receive requests over network (1030) from aclient application (for example, executing on another computer (1002))and responding to the received requests by processing the said requestsin an appropriate software application. In addition, requests may alsobe sent to the computer (1002) from internal users (for example, from acommand console or by other appropriate access method), external orthird-parties, other automated applications, as well as any otherappropriate entities, individuals, systems, or computers.

Each of the components of the computer (1002) can communicate using asystem bus (1003). In some implementations, any or all of the componentsof the computer (1002), both hardware or software (or a combination ofhardware and software), may interface with each other or the interface(1004) (or a combination of both) over the system bus (1003) using anapplication programming interface (API) (1012) or a service layer (1013)(or a combination of the API (1012) and service layer (1013). The API(1012) may include specifications for routines, data structures, andobject classes. The API (1012) may be either computer-languageindependent or dependent and refer to a complete interface, a singlefunction, or even a set of APIs. The service layer (1013) providessoftware services to the computer (1002) or other components (whether ornot illustrated) that are communicably coupled to the computer (1002).The functionality of the computer (1002) may be accessible for allservice consumers using this service layer. Software services, such asthose provided by the service layer (1013), provide reusable, definedbusiness functionalities through a defined interface. For example, theinterface may be software written in JAVA, C++, or other suitablelanguage providing data in extensible markup language (XML) format orother suitable format. While illustrated as an integrated component ofthe computer (1002), alternative implementations may illustrate the API(1012) or the service layer (1013) as stand-alone components in relationto other components of the computer (1002) or other components (whetheror not illustrated) that are communicably coupled to the computer(1002). Moreover, any or all parts of the API (1012) or the servicelayer (1013) may be implemented as child or sub-modules of anothersoftware module, enterprise application, or hardware module withoutdeparting from the scope of this disclosure.

The computer (1002) includes an interface (1004). Although illustratedas a single interface (1004) in FIG. 10, two or more interfaces (1004)may be used according to particular needs, desires, or particularimplementations of the computer (1002). The interface (1004) is used bythe computer (1002) for communicating with other systems in adistributed environment that are connected to the network (1030).Generally, the interface (1004 includes logic encoded in software orhardware (or a combination of software and hardware) and operable tocommunicate with the network (1030). More specifically, the interface(1004) may include software supporting one or more communicationprotocols associated with communications such that the network (1030) orinterface's hardware is operable to communicate physical signals withinand outside of the illustrated computer (1002).

The computer (1002) includes at least one computer processor (1005).Although illustrated as a single computer processor (1005) in FIG. 10,two or more processors may be used according to particular needs,desires, or particular implementations of the computer (1002).Generally, the computer processor (1005) executes instructions andmanipulates data to perform the operations of the computer (1002) andany algorithms, methods, functions, processes, flows, and procedures asdescribed in the instant disclosure.

The computer (1002) also includes a memory (1006) that holds data forthe computer (1002) or other components (or a combination of both) thatcan be connected to the network (1030). For example, memory (1006) canbe a database storing data consistent with this disclosure. Althoughillustrated as a single memory (1006) in FIG. 10, two or more memoriesmay be used according to particular needs, desires, or particularimplementations of the computer (1002) and the described functionality.While memory (1006) is illustrated as an integral component of thecomputer (1002), in alternative implementations, memory (1006) can beexternal to the computer (1002).

The application (1007) is an algorithmic software engine providingfunctionality according to particular needs, desires, or particularimplementations of the computer (1002), particularly with respect tofunctionality described in this disclosure. For example, application(1007) can serve as one or more components, modules, applications, etc.Further, although illustrated as a single application (1007), theapplication (1007) may be implemented as multiple applications (1007) onthe computer (1002). In addition, although illustrated as integral tothe computer (1002), in alternative implementations, the application(1007) can be external to the computer (1002).

There may be any number of computers (1002) associated with, or externalto, a computer system containing computer (1002), wherein each computer(1002) communicates over network (1030). Further, the term “client,”“user,” and other appropriate terminology may be used interchangeably asappropriate without departing from the scope of this disclosure.Moreover, this disclosure contemplates that many users may use onecomputer (1002), or that one user may use multiple computers (1002).

Although only a few example embodiments have been described in detailabove, those skilled in the art will readily appreciate that manymodifications are possible in the example embodiments without materiallydeparting from this invention. Accordingly, all such modifications areintended to be included within the scope of this disclosure as definedin the following claims. In the claims, any means-plus-function clausesare intended to cover the structures described herein as performing therecited function(s) and equivalents of those structures. Similarly, anystep-plus-function clauses in the claims are intended to cover the actsdescribed here as performing the recited function(s) and equivalents ofthose acts. It is the express intention of the applicant not to invoke35 U.S.C. § 112(f) for any limitations of any of the claims herein,except for those in which the claim expressly uses the words “means for”or “step for” together with an associated function.

What is claimed is:
 1. A method, comprising: obtaining, by a computerprocessor, a sonic waveform for each of a plurality of source andreceiver positions along a borehole; obtaining, by the computerprocessor, a sonic wave propagation velocity of a target event for theplurality of source and receiver positions along the borehole;performing, by the computer processor, a linear moveout correction onthe sonic waveforms based, at least in part, on the sonic wavepropagation velocity of the target event for the plurality of source andreceiver positions along the borehole; stacking, by the computerprocessor, the linear moveout corrected sonic waveforms to generate astacked waveform at the plurality of source and receiver positions alongthe borehole; determining, by the computer processor, an arrival-time ofthe target event on the stacked waveform for each of the plurality ofsource and receiver positions along the borehole based, at least in parton an extremum of a first objective function based on the stackedwaveforms; predicting, by the computer processor, a candidatearrival-time of the target event for the sonic waveform at the pluralityof source and receiver positions based, at least in part, on thearrival-time of the target event on the stacked waveform for theplurality of positions, and the sonic wave propagation velocity of thetarget event for the plurality of source and receiver positions withinthe borehole; and determining, by the computer processor, anarrival-time for the target event on the sonic waveform at the pluralityof source and receiver positions within the borehole based, at least inpart on the candidate arrival-time of the target event and an extremumof a second objective function.
 2. The method of claim 1, furthercomprising: determining, by the computer processor, a well path throughthe subterranean region of interest using the attribute volume; andperforming the well path using a drilling system.
 3. The method of claim1, wherein the obtaining, by a computer processor, a sonic waveform fora plurality of source and receiver positions along a borehole furthercomprises band-pass filtering the sonic waveform.
 4. The method of claim1, wherein the obtaining, by the computer processor, a sonic wavepropagation velocity of the target event for a plurality of positionsalong the borehole further comprises: determining the sonic wavepropagation velocity of the target event from the sonic waveforms for aplurality of source and receiver positions along a borehole.
 5. Themethod of claim 1, wherein the first objective function is based, atleast in part, on one or more reference stacked waveforms, and a currentstacked waveform for which the arrival-time of the target event is to bedetermined.
 6. The method of claim 1, wherein the extremum of the firstobjective function, and the extremum of the second objective function,is selected from the group consisting of a maximum of the objectivefunction, and a minimum of the objective function.
 7. The method ofclaim 5, wherein the first objective function further comprise termsquantifying one or more of the semblance, phase consistency, energyratio, and time-pick consistency, between the reference stacked waveformand the current stacked waveform.
 8. The method of claim 1, wherein theobtaining, by a computer processor, a sonic waveform for a plurality ofsource and receiver positions within a borehole further comprises:obtaining, an initial arrival-time and a time-window enclosing theinitial arrival-time.
 9. The method of claim 1: wherein, the firstobjective function is based, at least in part on the portion of thestacked waveform within the first time-window enclosing the initialarrival-time.
 10. The method of claim 1: wherein predicting, by thecomputer processor, a candidate arrival-time for the sonic waveform atthe plurality of source and receiver positions based, at least in part,on the arrival-time on the stacked waveform for a plurality ofpositions, further comprises: incrementing, the arrival time-pick on thestacked waveform by the product of the sonic wave propagation velocityof the target event, and the distance between the position of the sonicwaveform and the position of the stacked waveform.
 11. The method ofclaim 1, wherein the second objective function is based, at least inpart, on one or more reference sonic waveforms, and a current sonicwaveform for which the arrival-time is to be determined.
 12. The methodof claim 1, wherein the second objective function further comprise termsquantifying one or more of the semblance, phase consistency, energyratio, and time-pick consistency, between one or more reference sonicwaveforms and a current sonic waveform.
 13. The method of claim 1:wherein, the second objective function is based, at least in part on theportion of the reference sonic waveforms within the second time-windowenclosing the candidate arrival-time.
 14. A non-transitory computerreadable medium storing instructions executable by a computer processor,the instructions comprising functionality for: obtaining, a sonicwaveform for each of a plurality of source and receiver positions alonga borehole; obtaining, a sonic wave propagation velocity of a targetevent for the plurality of source and receiver positions along theborehole; performing, a linear moveout correction on the sonic waveformsbased, at least in part, on the sonic wave propagation velocity of thetarget event for the plurality of source and receiver positions alongthe borehole; stacking the linear moveout corrected sonic waveforms togenerate a stacked waveform at the plurality of source and receiverpositions along the borehole; determining, an arrival-time of the targetevent on the stacked waveform for each of the plurality of source andreceiver positions along the borehole based, at least in part on anextremum of a first objective function based on the stacked waveforms;predicting, a candidate arrival-time of the target event for the sonicwaveform at the plurality of source and receiver positions based, atleast in part, on the arrival-time of the target event on the stackedwaveform for the plurality of positions, and the sonic wave propagationvelocity of the target event for the plurality of source and receiverpositions within the borehole; and determining, an arrival-time for thetarget event on the sonic waveform at the plurality of source andreceiver positions within the borehole based, at least in part on thecandidate arrival-time of the target event and an extremum of a secondobjective function sonic waveforms.
 15. The non-transitory computerreadable medium of claim 14, wherein the obtaining, a sonic waveform fora plurality of source and receiver positions along a borehole furthercomprises band-pass filtering the sonic waveform.
 16. The non-transitorycomputer readable medium of claim 14, wherein the first objectivefunction is based, at least in part, on one or more reference stackedwaveforms, and a current stacked waveform for which the arrival-time ofthe target event is to be determined.
 17. The non-transitory computerreadable medium of claim 14, wherein the first objective functionfurther comprise terms quantifying one or more of the semblance, phaseconsistency, energy ratio, and time-pick consistency, between thereference stacked waveform and the current stacked waveform.
 18. Thenon-transitory computer readable medium of claim 14: wherein predicting,a candidate arrival-time for the sonic waveform at the plurality ofsource and receiver positions based, at least in part, on thearrival-time on the stacked waveform for a plurality of positions,further comprises: incrementing, the arrival time-pick on the stackedwaveform by the product of the sonic wave propagation velocity of thetarget event, and the distance between the position of the sonicwaveform and the position of the stacked waveform.
 19. Thenon-transitory computer readable medium of claim 14, wherein the secondobjective function is based, at least in part, on one or more referencesonic waveforms, and a current sonic waveform for which the arrival-timeis to be determined.
 20. The non-transitory computer readable medium ofclaim 14, wherein the second objective function further comprise termsquantifying one or more of the semblance, phase consistency, energyratio, and time-pick consistency, between one or more reference sonicwaveforms and a current sonic waveform.